Applied Calc

Question

Write the function below in the form Upper P equals Upper P Subscript 0 Baseline a Superscript t. Is this exponential growth or exponential decay?

P=2e^-2.3t

Round the base of the exponential function, a, to four decimal places.

Answer 1

This is the form P=P₀a^t

 

At t=0, e^-2.3t=e⁰=1, (anything to the zeroth power is just one)

 

So, P₀=2, at t=0 (ie. before exponential decay begins)

      P₀=2 would be called the "amplitude" or max value of the function

Then a^t has the form of a decay function or attenuation function

Let    a=e^-2.3 = 1/(e^2.3) = constant

Then a^t=e^-2.3t  since  (c^d)^g=c^dg  (law of exponents)

        a^t=1/(e^2.3t)  decreases with increasing t

Therefore, again, this function most definitely decays.